IMPUTACIÓN DE DATOS EN DISEÑOS SWITCHBACK USANDO UN MODELO MIXTO CON ERRORES CORRELACIONADOS

DATA IMPUTATION IN SWITCHBACK DESIGNS USING A MIXED MODEL WITH CORRELATED ERRORS

Se trata el problema de imputar mediciones individuales en datos provenientes de diseños switchback con errores correlacionados, teniendo en cuenta la propuesta de Barroso et al. (1998), donde se considera el BLUP (Best Linear Unbiased Predictor) para la imputación de datos. Se hizo uso de los valores propios de las matrices de cuadrados medios de los errores de las predicciones para comparar las estructuras de covarianza σ²I, AR(1) y CS asociadas a los errores. Los resultados sugieren que las dos primeras estructuras son más adecuadas que la tercera.

The problem of predicting individual measurements in switchback designs with correlated errors is considered. The predictions and imputations are done using the BLUP (Best Linear Unbiased Predictions), which have been suggested by Barroso et al. (1998). Three covariance structures were compared by the eigenvalues of the matrices of mean square errors. The results suggest that structures σ²I and AR(1) are better than CS.

Imputación de datos en diseños switchback usando un modelo mixto con errores correlacionados Data Imputation in Switchback Designs Using a Mixed Model with Correlated Errors LUIS FERNANDO GRAJALES¹, LUIS ALBERTO LÓPEZ ²

¹Universidad Nacional de Colombia, Departamento de Estadística, Bogotá, Profesor Asistente. E-mail: lfgrajalesh@unal.edu.co
²Universidad Nacional de Colombia, Departamento de Estadística, Bogotá, Profesor Asociado. E-mail: lalopezp@unal.edu.co

---

Resumen

Se trata el problema de imputar mediciones individuales en datos provenientes de diseños switchback con errores correlacionados, teniendo en cuenta la propuesta de Barroso et al. (1998), donde se considera el BLUP (Best Li- near Unbiased Predictor) para la imputación de datos. Se hizo uso de los valores propios de las matrices de cuadrados medios de los errores de las predicciones para comparar las estructuras de covarianza σ²I, AR(1) y CS asociadas a los errores. Los resultados sugieren que las dos primeras estructuras son más adecuadas que la tercera.

Palabras clave: datos faltantes, mínimos cuadrados generalizados, BLUP, estructura de covarianza.

---

Abstract

The problem of predicting individual measurements in switchback designs with correlated errors is considered. The predictions and imputations are done using the BLUP (Best Linear Unbiased Predictions), which have been suggested by Barroso et al. (1998). Three covariance structures were compared by the eigenvalues of the matrices of mean square errors. The results suggest that structures σ²I and AR(1) are better than CS.

Key words: Missing data, Generalized least squares, Best linear unbiased prediction, Covariance structure.

---

Texto completo disponible en PDF

---

Referencias

1. Barroso, L., Bussab, W. & Knott, M. (1998), "Best Linear Unbiased Predictor in the Mixed Model with Incomplete Data", Commun. Statis. - Theory Meth. 27(1), 121- 129.

2. Carriere, K. (1994), "Incomplete Repeated Measures Data Analysis in the Presence of Treatments Effects", J. Am. Stat. Assoc.89, 680- 686.

3. Ebbutt, A. (1984), "Three-Period Crossover Design for Two Treatments", Biome- trics 40, 219- 224.

4. Grajales, L. (2006), Imputación de datos en modelos mixtos con errores correlacionados: caso de diseños switchback, Tesis de maestría, Ciencias-Estadística, Universidad Nacional de Colombia, sede Bogotá.

5. Jones, B. & Kenward, M. (2003), Design and Analysis of Cross-Over Trials, 2 edn, Chapman and Hall.

6. Li, C. (1964), Introduction to Experimental Statistics, McGraw-Hill.

7. Li, J. (1995), Analysis of Switchback Designs, Technical report, Louisiana State University.

8. Little, R. & Rubin, D. B. (2002), Statistical Analysis with Missing Data, 2 edn, Jonh Wiley & Sons.

9. Lucas, H. L. (1956), "Switchback Trials for more than two Treatments", Journal of Dairy Science 39, 146- 154.

10. Macchiavelli, R. (1997), Analysis of switch-back designs in dairy experiments, in "5^th Meeting of the International Biometric Society Network for Central America, the Caribbean, Mexico, Colombia and Venezuela".

11. Matthews, J. (1988), "Recent Developments in Crossover Designs", International Statistical Review 56(2), 117- 127.

12. Oman, S. & Seiden, E. (1988), "Switch-back Designs", Biometrika 75, 81- 89.

13. Richardson, B. & Flack, V. (1996), "The Analysis of Incomplete Data in Threeperiod Two-treatment Cross-over Design for Clinical Trials", Statistics in Medicine 15, 127- 143.

14. SAS (2005), SAS/STAT software: changes and enhancements.

15. Searle, S., Casella, G. & McCulloch, C. (1992), Variance Components, Jonh Wiley & Sons.

16. Tempelman, R. (2004), "Experimental Design and Statistical Methods for Classical and Bioequivalence Hypothesis Testing with an Application to Dairy Nutrition Studies", J. Anim. Sci. 82 (E. Suppl.), E162- E172.

17. Wolfinger, R. D. (1993), "Covariance Structure Selection in GeneralMixedModels", Communication in Statistics, Simulation and Computation 22, 1079- 1106.

18. Yates, F. (1933), "The Analysis of Replicated Experiments when the Field Results are Incomplete", Annals of Eugenics pp. 27- 33.